Integration points and weights with orthogonal polynomials
This means that the matrix \( L_{ik} \) has an inverse with the properties
$$
\begin{equation*}
\hat{L}^{-1}\hat{L} = \hat{I}.
\end{equation*}
$$
Multiplying both sides of Eq.
(16) with \( \sum_{j=0}^{N-1}L_{ji}^{-1} \) results in
$$
\begin{equation}
\sum_{i=0}^{N-1}(L^{-1})_{ki}Q_{N-1}(x_i)=\alpha_k.
\tag{17}
\end{equation}
$$